A363188 Prime numbers that are the exact average of four consecutive odd semiprimes.

53, 67, 89, 199, 223, 277, 349, 439, 449, 461, 487, 491, 499, 523, 557, 569, 643, 683, 877, 883, 929, 941, 1069, 1153, 1259, 1361, 1471, 1487, 1733, 1787, 1901, 1933, 1951, 2111, 2129, 2251, 2297, 2311, 2371, 2521, 2557, 2689, 2777, 2797, 2861, 2917, 2939, 3037, 3041, 3253, 3259, 3271, 3407

Offset

1,1

Links

Table of n, a(n) for n=1..53.

Example

53 is a term because (49 + 51 + 55 + 57)/4 = 53 is prime.
67 is a term because (57 + 65 + 69 + 77)/4 = 67 is prime.

Maple

OP:= select(isprime, [seq(i, i=3..10000, 2)]):
OSP:= sort(select(`<=`, [seq(seq(OP[i]*OP[j], j=1..i), i=1..nops(OP))], 3*OP[-1])):
SA:= [seq(add(OSP[i+j], j=0..3)/4, i=1..nops(OSP)-3)]:
select(t -> t::integer and isprime(t), SA); # Robert Israel, May 21 2023

Mathematica

Select[Plus @@@ Partition[Select[Range[1, 3500, 2], PrimeOmega[#] == 2 &], 4, 1] / 4, PrimeQ] (* Amiram Eldar, May 21 2023 *)

Prog

(Python)
from itertools import count, islice
from sympy import factorint, isprime
def semiprime(n): return sum(e for e in factorint(n).values()) == 2
def nextoddsemiprime(n): return next(k for k in count(n+1+(n&1), 2) if semiprime(k))
def agen(): # generator of terms
    osp = [9, 15, 21, 25]
    while True:
        q, r = divmod(sum(osp), len(osp))
        if r == 0 and isprime(q):
            yield q
        osp = osp[1:] + [nextoddsemiprime(osp[-1])]
print(list(islice(agen(), 53))) # Michael S. Branicky, May 21 2023

Crossrefs

Cf. A000040, A046315.

Cf. A363074, A363187.

Sequence in context: A115936 A182571 A034965 * A341662 A160029 A229663

Adjacent sequences: A363185 A363186 A363187 * A363189 A363190 A363191

Keyword

nonn

Author

Elmo R. Oliveira, May 20 2023

Status

approved